The phrase "to designate an agent" means to choose or appoint someone to act on your behalf or represent you in a specific task or responsibility. Full definition
The real estate representative acted as designated agent for the sellers of the property. (nar.realtor)
This is how a designated agency brokerage can represent a buyer and a seller in a single transaction with full agency representation to both parties, when both parties have different designated agents. (nsrec.ns.ca)
We can be the sole designated agent, but that's the agent of the brokerage to the client and not of the client. (remonline.com)